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 A248705 The cubes related to the strictly increasing subsequence of A053668(n), n >= 1. 1
 1, 8, 27, 64, 343, 729, 2744, 3375, 6859, 35937, 46656, 148877, 287496, 438976, 778688, 2985984, 3869893, 8489664, 34645976, 43986977, 58863869, 75686967, 398688256, 426957777, 485587656, 596947688, 835896888, 1693669888, 2548895896, 2954987875, 4758586568 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The triangular numbers of this form are at A246753. The squares of this form are at A248648. LINKS Chai Wah Wu, Table of n, a(n) for n = 1..139 (first 116 terms from K. D. Bajpai) EXAMPLE a(4) = 64 = 4*4*4, which is a cube. Product of its digits = 6*4 = 24. a(5) = 343 = 7*7*7, which is a cube. Product of its digits = 3*4*3 = 36. Since 36 > 24, 64 and 343 appear in the sequence. As suggested by Wolfdieter Lang, examples further clarified: (Start) A053668 is sieved (from left to right): 1, 2, 3, 4, 5, 6, 7, 8, 9, ....(numbers: k) 1, 8, 27, 64, 125, 216, 343, 512, 729, ....(cubes: k^3) 1, 8, 14, 24, 10, 12, 36, 10, 126, ....(prod of digits of k^3) 1, 8, 14, 24, X, X, 36, X, 126, ....(sieved products) and related leftover cubes are: 1, 8, 27, 64, 343, 729, ....(leftover cubes) (End) MATHEMATICA A248705 = {}; t = 0; Do[s = Apply[Times, IntegerDigits[n^3]]; If[s > t, t = s; AppendTo[A248705, n^3]], {n, 1, 10^4}]; A248705 PROG (PARI) \\ For b-file c = 0; k = 0; for(n=1, 5*10^8, d = digits(n^3); p = prod(i = 1, #d, d[i]); while(p > k, c++; print(c, " ", n^3); k = p)) (Python) from operator import mul from functools import reduce A248705_list, x, m = [], 0, [6, -6, 1, 0] for _ in range(10**9): for i in range(3): m[i+1]+= m[i] xn = reduce(mul, [int(d) for d in str(m[-1])], 1) if xn > x: x = xn A248705_list.append(m[-1]) # Chai Wah Wu, Nov 19 2014 CROSSREFS Cf. A000578, A053668, A230041, A246569, A246753, A248648. Sequence in context: A121652 A112989 A018832 * A030293 A030479 A061096 Adjacent sequences: A248702 A248703 A248704 * A248706 A248707 A248708 KEYWORD nonn,base AUTHOR K. D. Bajpai, Oct 13 2014 STATUS approved

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Last modified June 20 14:54 EDT 2024. Contains 373526 sequences. (Running on oeis4.)